I was supposed to arrange some species in order of increasing polarizability. I used the estimated atomic radius without checking, and this is what I got:
$$Kr

Question

I was supposed to arrange some species in order of increasing polarizability.  I used the estimated atomic radius without checking, and this is what I got:
$$Kr<Ne<H_2<O_2<N_2<Cl_2$$
a) Is my reasoning flawed?
b) Did I make any obvious errors when ranking the species?

anonymous · Answer

Hmm.

a) What is your reasoning?  It would be helpful to post that as well.  But just for your benefit here is mine, all leading up to an answer to your question:

  Consider the bond length, and the dipole attractions between atoms: H2 for example.  This has no net charge, and the bond-lengths are equal.  But consider another molecule, say [H2SO4]^-2 (the sulfuric acid).  Now, clearly the bond lengths will differ drastically.  Consider SO4: it's tetrahedral in shape.  H2SO4 is not, and those two Hs pull electrons ever so slightly away from the S.  But those Hs have a definite dipole moment, or in other words a slight positive charge, because of the O atoms.

The atomic radius would certainly not give you the correct answer alone, but knowing several properties of the periodic table could.  For instance, F is the most electronegative element (meaning it is the most electron-greedy), and electronegativity steadily decreases as you get further away from F.  

Taking that into account I think you did fairly well in ranking the elements.  No obvious errors that I can see.

anonymous · Answer

My reasoning is as follows.  None of the substances are polar.  London dispersion forces are going to be the only forces holding these substances together.  LDFs are proportional to polarizability.  All else being equal, polarizability is proportional to the size of the molecule.  (I'm pretty sure all of the substances are gases at "room temperature" and 1 atm.)  Monoatomic molecules ought to be smaller than diatomic molecules (I was about to go to sleep) so I estimated the noble gases would be smallest.  From there, I simply estimated atomic radius without verifying the information (the paper copy of my periodic table does not list this information, and I didn't feel like looking it up).

In any case, thanks for taking a look at this.  It sounds like my approach was not utter broken.

anonymous · Answer

"Utter" should be "utterly".  (Confound the lack of edit functionality to the cheese factory!)